Disjoint directed cycles with specified lengths in directed bipartite graphs

Abstract Let D = ( V 1 , V 2 ; A ) be a directed bipartite graph with | V 1 | = | V 2 | = n ≥ 2 . Let a ( v ) denote the degree of v in D for all v ∈ V ( D ) . Suppose that a ( x ) + a ( y ) ≥ 3 n for all x ∈ V 1 and y ∈ V 2 . Then for any k positive integers n 1 , … , n k with n 1 + ⋯ + n k ≤ n , D contains k disjoint directed cycles of lengths 2 n 1 , 2 n 2 , … , 2 n k , respectively, unless n is even and D is isomorphic to an exceptional directed bipartite graph. This confirms a conjecture posed by Hong Wang in 2001.